When you get all 16 badges, go to Oak's lab and he'll give you the HM
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To get rock climb in HG/SS you have to beat Blue's Pokemon gym in Veridian City first. Then, go talk to Professor Oak. He will give you the HM rock climb. Note: If you trade a Pokemon from D/P/P , even if you taught it rock climb, you cant use it until you beat Varidian gym.
D/P: HM04 Strength: Lost Tower HM08 Rock Climb: Route 217 in snow Pt: HM04 Strength: Iron Island from Riley HM08 Rock Climb: Route 217 in snow HG/SS: HM04 Strength: Route 42 from Hiker HM08 Rock Climb: Pallet Town from Prof. Oak
After you beat all 16 badges go to Proffesor Oak's Lab and he will give it to you. Hope this helped ya
The HM Rock climb is on route 217.
Go to mount silver (With a Pokemon that knows rock climb) climb to the top, and challenge Red.